Linear Algebra (4th Edition)
by Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence
Average Customer Review: 
Hardcover
(11 November, 2002)
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Reviews (18)
FRUSTRATING
First of all, a little background on myself. I am a college sophomore and an overachiever in mathematics for my entire life. I am currently taking a Linear Algebra course that uses this book. We have just finished chapter 2 and I am ready to throw my book in the fire.
Before I talk about why I hate this book I will first give some positives.
1. The book is very concise. A lot of material is covered in relatively few pages. There are not many pictures or graphs to clutter up the pages.
2. This book covers the material very thoroughly. Everything is defined and everything has a clear proof, except for a few theorems which are left as exercises.
Now for the bad...
1. The thing that drives me insane about this book is the lack of decent examples. Since this is new material to myself and many others, it really helps to aid understanding if there are well-explained examples to accompany the new information. Most of the examples in the text are either WAY too simple, or are left thoroughly unexplained. Sometimes I feel like a toddler trying to learn addition, but all I have to go on is that 0+1=1.
2. There is no answer key. If there were an answer key for the problems it would more than make up for the lack of examples, but instead we are left with about 5% of the answers to the simplest exercises.
3. There is little explanation of the computational aspects of linear algebra. This goes hand-in-hand with the poor examples. If the text spent as much time explaining how to use the material as it does explaining where it is derived from then it would be a lot easier to understand.
That's all I can think of for now. This is definitely not the worst textbook in the world, but my opinion is that the bad outweighs the good and it should be avoided by anyone new to Linear Algebra.
Hope this helps.
An Extremely Frustrating Book
I have never seen a book which hides so many important details (and even basic definitions) in exercises. This book was terrible to learn from and even worse as a reference. It also omits or glosses over a number of important topics including quadratic forms and matrix norms.
Excellent Text for Theory
For reference, I have done only a few problems, and haven't really read other books on Linear Algebra.
That aside, I can still attest that this is a superb book. The proofs throughout are clear, short, straightforward, and remarkably free of even trivial errors. Definitions are generally introduced when the motivation is sufficient and the organization is undoubtly sensible (from theoretical perspective). Despite the heavy emphasis on theory, there are well-developed examples as diverse as linear diffeq, economics, and einstein's relativity. These extra sections can be skipped without loss of continuity. As far as the problems go, they progress from trivial to more difficult, interesting proofs.
My only gripe is that the authors take little initiative to give a geometric interpretation of results. especially in the chapter on inner products. It is much easier to remember visual pictures in your mind then a wordy thereom.
If you plan to read the book, I would recommend two semesters of calculus and a preliminary course in abstract mathematics (sets and proofs).
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